Graduate School of Informatics, Kyoto University, Gokasho, 611-0011 Uji, Kyoto, Japan.
Comput Math Methods Med. 2013;2013:931507. doi: 10.1155/2013/931507. Epub 2013 Apr 18.
With the advent of novel biomedical 3D image acquisition techniques, the efficient and reliable analysis of volumetric images has become more and more important. The amount of data is enormous and demands an automated processing. The applications are manifold, ranging from image enhancement, image reconstruction, and image description to object/feature detection and high-level contextual feature extraction. In most scenarios, it is expected that geometric transformations alter the output in a mathematically well-defined manner. In this paper we emphasis on 3D translations and rotations. Many algorithms rely on intensity or low-order tensorial-like descriptions to fulfill this demand. This paper proposes a general mathematical framework based on mathematical concepts and theories transferred from mathematical physics and harmonic analysis into the domain of image analysis and pattern recognition. Based on two basic operations, spherical tensor differentiation and spherical tensor multiplication, we show how to design a variety of 3D image processing methods in an efficient way. The framework has already been applied to several biomedical applications ranging from feature and object detection tasks to image enhancement and image restoration techniques. In this paper, the proposed methods are applied on a variety of different 3D data modalities stemming from medical and biological sciences.
随着新型生物医学三维图像采集技术的出现，高效可靠地分析体积图像变得越来越重要。数据量巨大，需要自动化处理。应用范围广泛，从图像增强、图像重建和图像描述到目标/特征检测和高级上下文特征提取。在大多数情况下，预期几何变换以数学上定义良好的方式改变输出。在本文中，我们重点研究三维平移和旋转。许多算法依赖于强度或低阶张量样描述来满足这一需求。本文提出了一个基于数学物理和调和分析中转移到图像分析和模式识别领域的数学概念和理论的通用数学框架。基于两个基本操作，即球张量微分和球张量乘法，我们展示了如何以有效的方式设计各种三维图像处理方法。该框架已经应用于多种生物医学应用，包括特征和目标检测任务、图像增强和图像恢复技术。在本文中，所提出的方法应用于各种不同的源自医学和生物学科学的三维数据模态。
